Which decimal is equivalent to 1/7? Choices: (A)0.{17} (B)0.17 (C)0.142857 (D)0.{142857}

Calculate Decimal Equivalent: Step 1: Calculate 1 divided by 7 using long division to find the decimal equivalent. 1 divided by 7 equals approximately 0.142857 repeating. This is a repeating decimal, which means the same digits repeat indefinitely.Compare with Choices: Step 2: Compare the result from Step 1 with the given choices. The calculated decimal 0.142857 matches with choice (C) 0.142857 and (D) 0.{142857}, which indicates a repeating decimal pattern.Correct Notation for Repeating Decimals: Step 3: Determine the correct notation for repeating decimals among the choices. Choice (D) 0.{142857} correctly represents the repeating nature of the decimal, whereas choice (C) is just the decimal without indicating repetition.

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Which decimal is equivalent to $\frac{1}{7}$ ? $\newline$ Choices: $\newline$ (A) $0.\overline{17}$ $\newline$ (B) $0.17$ $\newline$ (C) $0.142857$ $\newline$ (D) $0.\overline{142857}$

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Math Problems

Grade 8

Checkpoint: Rational and irrational numbers

Full solution

Q. Which decimal is equivalent to

\frac{1}{7}

\newline

Choices:

\newline

(A)

0.\overline{17}

\newline

(B)

0.17

\newline

(C)

0.142857

\newline

(D)

0.\overline{142857}

Calculate Decimal Equivalent: Step $1$ : Calculate $1$ divided by $7$ using long division to find the decimal equivalent. $\newline$ $1$ divided by $7$ equals approximately $0.142857$ repeating. This is a repeating decimal, which means the same digits repeat indefinitely.
Compare with Choices: Step $2$ : Compare the result from Step $1$ with the given choices. The calculated decimal $0.142857$ matches with choice (C) $0.142857$ and (D) $0.\overline{142857}$ , which indicates a repeating decimal pattern.
Correct Notation for Repeating Decimals: Step $3$ : Determine the correct notation for repeating decimals among the choices. $\newline$ Choice (D) $0.\overline{142857}$ correctly represents the repeating nature of the decimal, whereas choice (C) is just the decimal without indicating repetition.